One of the principal sources of Caesar's authority is registration and licenses. The word license has its roots in the Latin word licit, which means "legal or permitted." The opposite of licit is illicit.
The current use of registering and licensing goes back to the days of the Roman Empire. Rome discovered she could make her conquered people submit to her authority in almost every sphere of life. Conquered people would fight in Rome's army and pay Roman taxes. But Rome had one stumbling block - she could not force the people to desert their religion and worship Roman deities.
Rome devised an ingenious plan to overcome this problem so that she could be sovereign - even over the religion of her conquered people. She started licensing religion. Rome declared her generosity and tolerance of all religions. She allowed the people to worship any god they chose and in any manner they desired. The people could raise their children according to the customs of their religion. They could even evangelize. All these privileges belonged to the people with one "minor" requirement: they must first obtain a license from the Roman government. Through this registration procedure, their religion became a licit religion under the sovereignty of the Roman Empire.
Judaism, for instance, was a "licensed religion" with special privileges. Jews could freely practice their religious customs and were exempt from participating in the Emperor's cult. Christianity, however, soon became an "illegal religion" because they would not meet the requirement to register with Caesar.
The principle behind the Christians' refusal to register or obtain a license from Caesar is that the lesser authority never licenses the greater authority. For a Christian to acknowledge that they must seek Caesar's approval, Caesar's license, would be to acknowledge Caesar's authority and lordship over them. And that was exactly Rome's intent. Their licensing scheme was designed to make Caesar lord over every sphere of life. Early Christians refused Caesar's licensing programs, not just with words, but with their very lives, proclaiming that Jesus Christ, not Caesar, is Lord.
To register anything, including a name, with Caesar, is to acknowledge the lordship of Caesar. Since Jesus is our Lord, we should be registering with God, not Caesar.